This invention relates generally to neural networks and more particularly to circuits which model the behavior of biological neurons.
As is known in the art, there exists a class of networks referred to as neural networks which model the behavior of certain human functions. Electronic neural networks have been used to implement mathematical or engineering abstractions of biological neurons. Circuits emulating biological neurons are typically implemented using digital circuits that operate up to a million times faster than actual neurons or with software which simulates the behavior of a biological neuron. One problem with the digital circuit approach, however is that it does not utilize life-like principles of neural computation. Furthermore, a biological nervous system contains thousands or millions of interconnected neurons and thus the complexity of a biological nervous system results in a complex digital circuit.
Similarly, given the complexity of the biological systems, software simulations can take many hours or days even using presently available state-of the-art processing systems. Thus software systems are not appropriate for use in applications which require real time or close to real time performance from such systems
An electronic circuit that emulates the analog behavior of actual biological neurons, on the other hand, can perform simulations in real time. Thus, to overcome the above limitations with systems implemented using digital circuits or software, electronic circuit neural networks which use principles of neural computation which are more life-like than the digital circuit or software approaches have been developed.
This type of neural network interacts with real-world events in a manner which is the same as or similar to biological nervous systems and can be utilized in a variety of systems including but not limited to electronic and electromechanical systems, such as artificial vision devices and robotic arms. Such neural networks can also be used as research tools to better understand how biological neural networks communicate and learn.
Much of the effort directed toward producing electronic implementations of biological neurons have focused on emulating the input-output functional characteristics of the neuron, essentially treating the neuron as an abstracted black box. These implementations focus on circuits and techniques for generating an action potential in an attempt to simulate the actions neurons take to communicate with one another. One problem with past approaches, however, is that such approaches fail to properly take into account or model the means which actually produces the action potential in a biological neuron.
Some prior art techniques have produced analog integrated circuits that mimic the functional characteristics of real neuron cells, by isomorphically emulating the membrane conductances within an actual neuron cell body. Thus, one problem with prior art approaches is that they fail to include circuitry for the synapse through which neurons communicate and/or the prior art approaches fail to include circuitry for the dendrite which is the connection between the synapse and neuron cell body. Prior art systems also fail to include effective circuitry to implement the adaptation or learning functions of real neurons.
In one particular prior art technique, a model of one type of synapse referred to as a Hebbian Synapse was provided. In a Hebbian Synapse, stimulation of the pre-synaptic neuron causes the release of neurotransmitters from an axon terminal. These transmitters include amino acid glutamate and bind to corresponding receptors on the post-synaptic membrane causing ion channels to open up through these receptors. Glutamate binds to three types of receptors: N-methyl-D-aspartate (NMDA), quisqualate, and kainate. Long Term Potentiation (LTP) and Long Term Depression (LTD) are both mediated by the NMDA receptors, which carry primarily Ca2+ currents. The other receptors, termed the non-NMDA receptors, carry the remainder of the synaptic current, consisting mainly of Na+, with negligible Ca2+ content. These receptors are located on a spine head connected to the dendritic shaft.
The spine head can be represented or modeled as an electrical circuit which includes four parallel circuit legs. The total synaptic current consists of the sum of the NMDA and non-NMDA currents. There also exists a small leakage conductance and the capacitance that represents the membrane capacitance of the spine head. The current through the non-NMDA channels in response to a pre-synaptic stimulus is given by an alpha function:
Inon=(Enonxe2x88x92Vhead)xcexagptet/p1xe2x80x83xe2x80x83Equation 1
in which K=e/tp, e is the base of the natural logarithm, tp=1.5 ms, gp=0.5 nS, and Exe2x80x2non=0. It should be noted that non-NMDA receptor conductance is purely ligand (neurotransmitter) dependent. The NMDA conductance, on the other hand, is both ligand dependent, due to the binding of neurotransmitters released from the pre-synaptic neuron, and dependent on the spine head membrane voltage. The current through the NMDA receptors is given by:                               I          NMDA                      (            t            )                          =                              (                                          E                NMDA                            -                              V                head                                      )                    ⁢                                                    g                n                            ⁡                              (                                                      ⅇ                                          1                      t1                                                        -                                      ⅇ                                          1                      t1                                                                      )                                                    1              +                                                n                  ⁡                                      [                                          Mg                                              2                        +                                                              ]                                                  ⁢                                  ⅇ                                      -                    tVhead                                                                                                          Equation        ⁢                  xe2x80x83                ⁢        2            
Where xcfx841=80 ms, xcfx842=0.67 ms, xcex7=0.33 nMxe2x88x921, xcex3=0.06 mVxe2x88x921, ENMDA=0 and gn=0.2 nS. The voltage dependence of the NMDA receptor arises from the fact that the receptors are inhibited by magnesium ions Mg2+ having a binding rate constant which is dependent upon the spine head membrane voltage. Near the resting membrane potential, the NMDA receptor channels are almost completely blocked by the Mg2+ ions, and thus little current flows. As the spine head membrane becomes partially depolarized, the Mg2+ ions become dislodged and more NMDA current flows.
The post-synaptic flow of Ca2+ ions through the NMDA receptor channels is crucial for the induction of LTP and LTD. Upon entering the dendritic spine, the Ca2+ ions trigger a series of events that lead to the induction and maintenance of LTP or LTD. The precise mechanisms, however, are not well understood. One theory is that a second messenger, such as nitric oxide, is activated by the Ca2+ ions and certain calcium dependent proteins and then diffuses back to the pre-synaptic terminal, stimulating the release of more glutamate. Thus, this retrograde messenger operates as a positive feedback mechanism. This model is limited, however, in that it only explains LTP.
Another model suggests that rather than affecting pre-synaptic neurotransmitter release, the induction of LTP or LTD modulates the post-synaptic conductance of the non-NMDA receptor channels, which carry the bulk of synaptic current. This model also relies on the influx of Ca2+ ions into the dendritic spines through the NMDA channel. During high frequency simulation, the Ca2+ ions reach high concentrations in the compartmentalized spine head and preferentially activates a protein kinase. During low frequency simulation, lower concentrations are reached and a protein phosphatase is released. Both proteins act on a common phosphoprotein, which triggers LTP or LTD by modulating the non-NMDA receptor channel conductance.
It would, therefore, be desirable to provide an analog very large scale integrated (VLSI) circuit implementation of a biological neuron which includes circuitry for the synapse through which neurons communicate, and the dendrite which serves as the connection between the synapse and neuron cell body. It would also be desirable to provide a circuit which represents the means which actually produce the action potential in a biological neuron. It would also be desireable to include in an analog VLSI implementation of a biological neuron, circuitry for adaptation or learning.
In accordance with the present invention, a circuit which implements functions of a biological nervous system includes a plurality of neuron circuits and a plurality of synapse circuits. The synapse circuits are coupled to provide a path through which the plurality of neuron circuits communicate. Each of the plurality of neuron circuits include (1) a neuron cell membrane circuit, (2) a learning circuit coupled to said neuron cell membrane circuit; and (3) a dendrite circuit coupled to the neuron cell membrane circuit. Each of the synapse circuits include means for modifying the synaptic conductance With this particular arrangement, a neuron circuit which models a biological neuron circuit and in particular which emulates the neuron synapse is provided. By providing the neuron circuit with circuitry which allows adaptation or learning function to be performed, the neuron circuit of the present invention more closely models a biological neuron than prior art systems. The synapse circuit includes an NMDA channel circuit which is coupled in parallel with a non-NMDA channel circuit between first and second terminals of the synapse circuit. Also coupled in parallel between the first and second terminals of the synapse circuit in parallel with the NMDA and non-NMDA channel circuits is a storage element. The non-NMDA channel circuit controls the induction of LTP and LTD in the neuron circuit thereby emulating the response to a neurotransmitter in a biological neuron. In particular, the induction of LTP is characterized by a prolonged increase in the conductance of the non-NMDA receptor channel, while the induction of LTD is characterized by the decrease in conductance of the non-NMDA receptor channel. The NMDA channel circuit provides a current which is approximately proportional to the flow of magnesium ions (Ca2+) into the spine head. The NMDA circuit emulates the response to the neurotransmitter. This controls long term memory effects in biological systems. The response to the post-synaptic neuron gives a pairing effect meaning that an NMDA receptor receives signals from both pre- and post-synaptic neurons and provides a response thereto. In a biological neuron, non-NMDA xe2x80x9cchannelsxe2x80x9d carry sodium ions (Na+) which are abundant while NMDA xe2x80x9cchannelsxe2x80x9d regulate the flow of calcium ions (Ca2+) to the neuron. The calcium is the internal messenger. Once the calcium travels into the cell body, it triggers chemical reactions (referred to as xe2x80x9csecondary messengersxe2x80x9d) in the post-synaptic cell. These secondary messengers affect the non-NMDA channels by increasing or decreasing the transmission in the channel. The neuron circuit of the present invention emulates the calcium influx via the NMDA channels and generates a signal which controls the response of the non-NMDA circuits by controlling the number of channels in those circuits which are open or closed.
In accordance with a further aspect of the present invention, an integrated circuit which implements functions of a biological nervous system includes circuits designed to emulate the electrical characteristics of actual neurons. In particular, the circuits emulate the neuron cell membrane, the dendritic structure, and a synapse. In one embodiment, one particular type of synapse referred to as a Hebbian synapse is modeled. These circuits are more neuromorphic compared to most analog neural networks. The neuron cell membrane circuits include circuitry to represent the sodium and potassium ion channels in the membrane. The synapse circuits include circuit portions which correspond to different types of synaptic current channels. Moreover the neuron circuit design of the present invention includes circuits which modify the synaptic conductance, or strength of the neuron through a feedback mechanism. With this particular technique, an analog CMOS circuit implementation of an electrical model of a biological synapse is provided. In particular, the circuits emulate the synaptic modification, the learning mechanism, exhibited in certain types of neurons. This can be used in an artificial neural network that emulates neural computation in a manner which is more realistic than conventional electronic artificial neural networks. In one embodiment, the integrated circuit of the present invention is implemented using CMOS circuits.